`padic_pow_si`

Synopsis#include <flint/padic.h>

void padic_pow_si(padic_t rop, const padic_t op, slong e, const padic_ctx_t ctx)source

Sets rop to $op^e$ , reduced, for any integer $e$ , with $op^0 = 1$ . For $e < 0$ the unit is first inverted modulo $p^{N - ev}$ . If op is zero and $e \ne 0$ the result is zero, also for $e < 0$ . Assumes that $ev$ does not overflow a slong.

If the input $p^v u$ is only known modulo $p^N$ , then $x^e$ is only known modulo $p^{N + (e - 1)v}$ , which is a loss of precision when $v < 0$ (Precision and representation of p-adic numbers). The function computes the power of the stored value exactly and does not account for this.

Cite this page

The FLINT team, “padic_pow_si (padic.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/padic/padic_pow_si.html (generated 2026-11-02).

@misc{flint-doc-padic-padic-pow-si,
  author       = {{The FLINT team}},
  title        = {{padic\_pow\_si (padic.h)}},
  howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
  year         = {2026},
  url          = {https://flintlib.org/doc/padic/padic_pow_si.html},
  note         = {Generated 2026-11-02}
}

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